How To Cut A Sine Shape On A Cylinder
I assume you are having trouble with that curve. One way to create it would be to use edge loops and proportional editing. You want to make sure your cylinder has a slightly higher resolution, so the curve will be relatively smooth.

Go into edit mode and add an edge loop in the middle of your cylinder.
Select it with alt + your selection mouse button and search for checker deselect (my search button is F3). A new tab will appear, which lets you specify the offset etc. You want to only select the tips of your future curve.
Now, enable proportional editing by pressing O and hit G to move the vertices. You can adjust the editing radius with your mouse wheel and move the vertices forward until you have something that looks like half of a sinus curve.
Repeat these steps with the other half.
Now, create another edge loop underneath that looks the same by pressing ctrl + R and then E. Go into face select mode and select the curve with alt + selection button.
Extrude it and scale it inwards while locking the x-axis by pressing shift + X while scaling.